Can't tell you anything about Python specifically, but Rich Hickey (author of Clojure) gave a great talk on "Simple Made Easy" with reference to functional programming. Definitely worth watching to understand the potential benefits of FP, whichever language you plan to use.

Python fits into the concept of functional programming by itself as it has lot of language constructs that aid in doing this.
Generally, as your code becomes pythonic, it will contain certain amount of functional programming constructs/approaches. http://docs.python.org/howto/functional.html